Complexity analysisThe cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the ...
Cubic regularizationWorst-case complexityMatrix-free subproblem solversIn this paper we consider the problem of minimizing a smooth function by using the adaptive cubic regularized (ARC) framework. We focus on the computation of the trial step as a suitable approximate minimizer of the cubic model ...
We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian. Then based on this reformulation, we derive a variant of the (non-adaptive) CR provided a known Lipschitz ...
At each iteration a candidate search direction is determined by solving the affine scaling cubic regularization subproblem and the new iteration is strictly feasible by way of an interior backtracking technique. The global convergence and local superlinear convergence of the proposed algorithm are ...
The adaptive cubic regularization algorithms described in Cartis, Gould and Toint [Adaptive cubic regularisation methods for unconstrained optimization Part II: Worst-case function- and derivative-evaluation complexity, Math. Program. (2010), doi:10.1007/s10107-009-0337-y (online)]; [Part I: ...
We propose a first-order method to solve the cubic regularization subproblem (CRS) based on a novel reformulation. The reformulation is a constrained convex optimization problem whose feasible region admits an easily computable projection. Our reformulation requires computing the minimum eigenvalue of ...
Cubic regularizationFilter methodsSequential quadratic programmingGlobal convergenceIn this paper, we propose a filter sequential adaptive regularization algorithm using cubics (ARC) for solving nonlinear equality constrained optimization. Similar to sequential quadratic programming methods, an ARC subproblem with ...
The latter solves the subproblem in nested Krylov subspaces by a Lanczos-based method, which requires the storage of a dense matrix that can be comparable to or larger than the two dense arrays required by our approach if the problem is large or requires many Lanczos iterations. Finally, we ...
By using the Moreau-Yosida regularization and proximal method, a new trust region algorithm is proposed for nonsmooth convex minimization. Acubic subproblem with adaptive parameter is solved at each iteration. The global convergence and Q-superlinear convergence are established under some suitable ...
Riemannian optimizationManifold optimizationStochastic optimizationCubic regularizationVariance reductionWe propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient...